LMFDB - Embedded newform 966.4.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.65101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 28x - 29 $ x^3 - 28*x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.74846$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.54790 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.54790 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +9.09580 q^{10} -27.2964 q^{11} -12.0000 q^{12} -24.8381 q^{13} -14.0000 q^{14} -13.6437 q^{15} +16.0000 q^{16} +115.673 q^{17} +18.0000 q^{18} -37.6796 q^{19} +18.1916 q^{20} +21.0000 q^{21} -54.5927 q^{22} -23.0000 q^{23} -24.0000 q^{24} -104.317 q^{25} -49.6762 q^{26} -27.0000 q^{27} -28.0000 q^{28} +146.433 q^{29} -27.2874 q^{30} -250.032 q^{31} +32.0000 q^{32} +81.8891 q^{33} +231.346 q^{34} -31.8353 q^{35} +36.0000 q^{36} -43.4880 q^{37} -75.3591 q^{38} +74.5143 q^{39} +36.3832 q^{40} -309.265 q^{41} +42.0000 q^{42} -63.5876 q^{43} -109.185 q^{44} +40.9311 q^{45} -46.0000 q^{46} -59.3355 q^{47} -48.0000 q^{48} +49.0000 q^{49} -208.633 q^{50} -347.019 q^{51} -99.3525 q^{52} -167.696 q^{53} -54.0000 q^{54} -124.141 q^{55} -56.0000 q^{56} +113.039 q^{57} +292.865 q^{58} -19.7175 q^{59} -54.5748 q^{60} -195.376 q^{61} -500.063 q^{62} -63.0000 q^{63} +64.0000 q^{64} -112.961 q^{65} +163.778 q^{66} -511.263 q^{67} +462.692 q^{68} +69.0000 q^{69} -63.6706 q^{70} -68.8314 q^{71} +72.0000 q^{72} +904.894 q^{73} -86.9759 q^{74} +312.950 q^{75} -150.718 q^{76} +191.075 q^{77} +149.029 q^{78} -188.251 q^{79} +72.7664 q^{80} +81.0000 q^{81} -618.530 q^{82} -1022.92 q^{83} +84.0000 q^{84} +526.069 q^{85} -127.175 q^{86} -439.298 q^{87} -218.371 q^{88} +1057.12 q^{89} +81.8622 q^{90} +173.867 q^{91} -92.0000 q^{92} +750.095 q^{93} -118.671 q^{94} -171.363 q^{95} -96.0000 q^{96} -1744.68 q^{97} +98.0000 q^{98} -245.667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 10 q^{10} - 56 q^{11} - 36 q^{12} + 29 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} + 28 q^{17} + 54 q^{18} - 18 q^{19} + 20 q^{20} + 63 q^{21} - 112 q^{22} - 69 q^{23} - 72 q^{24} + 32 q^{25} + 58 q^{26} - 81 q^{27} - 84 q^{28} - 242 q^{29} - 30 q^{30} - 86 q^{31} + 96 q^{32} + 168 q^{33} + 56 q^{34} - 35 q^{35} + 108 q^{36} - 70 q^{37} - 36 q^{38} - 87 q^{39} + 40 q^{40} - 402 q^{41} + 126 q^{42} - 553 q^{43} - 224 q^{44} + 45 q^{45} - 138 q^{46} - 368 q^{47} - 144 q^{48} + 147 q^{49} + 64 q^{50} - 84 q^{51} + 116 q^{52} + 23 q^{53} - 162 q^{54} - 467 q^{55} - 168 q^{56} + 54 q^{57} - 484 q^{58} - 861 q^{59} - 60 q^{60} - 311 q^{61} - 172 q^{62} - 189 q^{63} + 192 q^{64} - 624 q^{65} + 336 q^{66} - 215 q^{67} + 112 q^{68} + 207 q^{69} - 70 q^{70} + 121 q^{71} + 216 q^{72} - 588 q^{73} - 140 q^{74} - 96 q^{75} - 72 q^{76} + 392 q^{77} - 174 q^{78} - 1418 q^{79} + 80 q^{80} + 243 q^{81} - 804 q^{82} - 352 q^{83} + 252 q^{84} - 827 q^{85} - 1106 q^{86} + 726 q^{87} - 448 q^{88} + 1275 q^{89} + 90 q^{90} - 203 q^{91} - 276 q^{92} + 258 q^{93} - 736 q^{94} - 3593 q^{95} - 288 q^{96} - 602 q^{97} + 294 q^{98} - 504 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 10 * q^10 - 56 * q^11 - 36 * q^12 + 29 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 + 28 * q^17 + 54 * q^18 - 18 * q^19 + 20 * q^20 + 63 * q^21 - 112 * q^22 - 69 * q^23 - 72 * q^24 + 32 * q^25 + 58 * q^26 - 81 * q^27 - 84 * q^28 - 242 * q^29 - 30 * q^30 - 86 * q^31 + 96 * q^32 + 168 * q^33 + 56 * q^34 - 35 * q^35 + 108 * q^36 - 70 * q^37 - 36 * q^38 - 87 * q^39 + 40 * q^40 - 402 * q^41 + 126 * q^42 - 553 * q^43 - 224 * q^44 + 45 * q^45 - 138 * q^46 - 368 * q^47 - 144 * q^48 + 147 * q^49 + 64 * q^50 - 84 * q^51 + 116 * q^52 + 23 * q^53 - 162 * q^54 - 467 * q^55 - 168 * q^56 + 54 * q^57 - 484 * q^58 - 861 * q^59 - 60 * q^60 - 311 * q^61 - 172 * q^62 - 189 * q^63 + 192 * q^64 - 624 * q^65 + 336 * q^66 - 215 * q^67 + 112 * q^68 + 207 * q^69 - 70 * q^70 + 121 * q^71 + 216 * q^72 - 588 * q^73 - 140 * q^74 - 96 * q^75 - 72 * q^76 + 392 * q^77 - 174 * q^78 - 1418 * q^79 + 80 * q^80 + 243 * q^81 - 804 * q^82 - 352 * q^83 + 252 * q^84 - 827 * q^85 - 1106 * q^86 + 726 * q^87 - 448 * q^88 + 1275 * q^89 + 90 * q^90 - 203 * q^91 - 276 * q^92 + 258 * q^93 - 736 * q^94 - 3593 * q^95 - 288 * q^96 - 602 * q^97 + 294 * q^98 - 504 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	4.54790	0.406777	0.203388	−	0.979098i	$-0.434805\pi$
$5$	4.54790	0.406777	0.203388	+	0.979098i	$0.434805\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	9.09580	0.287635
$11$	−27.2964	−0.748197	−0.374098	−	0.927389i	$-0.622048\pi$
$11$	−27.2964	−0.748197	−0.374098	+	0.927389i	$0.622048\pi$
$12$	−12.0000	−0.288675
$13$	−24.8381	−0.529912	−0.264956	−	0.964261i	$-0.585357\pi$
$13$	−24.8381	−0.529912	−0.264956	+	0.964261i	$0.585357\pi$
$14$	−14.0000	−0.267261
$15$	−13.6437	−0.234853
$16$	16.0000	0.250000
$17$	115.673	1.65028	0.825141	−	0.564927i	$-0.191096\pi$
$17$	115.673	1.65028	0.825141	+	0.564927i	$0.191096\pi$
$18$	18.0000	0.235702
$19$	−37.6796	−0.454962	−0.227481	−	0.973782i	$-0.573049\pi$
$19$	−37.6796	−0.454962	−0.227481	+	0.973782i	$0.573049\pi$
$20$	18.1916	0.203388
$21$	21.0000	0.218218
$22$	−54.5927	−0.529055
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	−104.317	−0.834533
$26$	−49.6762	−0.374704
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	146.433	0.937650	0.468825	−	0.883291i	$-0.344677\pi$
$29$	146.433	0.937650	0.468825	+	0.883291i	$0.344677\pi$
$30$	−27.2874	−0.166066
$31$	−250.032	−1.44861	−0.724306	−	0.689478i	$-0.757840\pi$
$31$	−250.032	−1.44861	−0.724306	+	0.689478i	$0.757840\pi$
$32$	32.0000	0.176777
$33$	81.8891	0.431972
$34$	231.346	1.16693
$35$	−31.8353	−0.153747
$36$	36.0000	0.166667
$37$	−43.4880	−0.193226	−0.0966132	−	0.995322i	$-0.530801\pi$
$37$	−43.4880	−0.193226	−0.0966132	+	0.995322i	$0.530801\pi$
$38$	−75.3591	−0.321707
$39$	74.5143	0.305945
$40$	36.3832	0.143817
$41$	−309.265	−1.17803	−0.589013	−	0.808123i	$-0.700483\pi$
$41$	−309.265	−1.17803	−0.589013	+	0.808123i	$0.700483\pi$
$42$	42.0000	0.154303
$43$	−63.5876	−0.225512	−0.112756	−	0.993623i	$-0.535968\pi$
$43$	−63.5876	−0.225512	−0.112756	+	0.993623i	$0.535968\pi$
$44$	−109.185	−0.374098
$45$	40.9311	0.135592
$46$	−46.0000	−0.147442
$47$	−59.3355	−0.184148	−0.0920742	−	0.995752i	$-0.529350\pi$
$47$	−59.3355	−0.184148	−0.0920742	+	0.995752i	$0.529350\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−208.633	−0.590104
$51$	−347.019	−0.952791
$52$	−99.3525	−0.264956
$53$	−167.696	−0.434620	−0.217310	−	0.976103i	$-0.569728\pi$
$53$	−167.696	−0.434620	−0.217310	+	0.976103i	$0.569728\pi$
$54$	−54.0000	−0.136083
$55$	−124.141	−0.304349
$56$	−56.0000	−0.133631
$57$	113.039	0.262673
$58$	292.865	0.663019
$59$	−19.7175	−0.0435084	−0.0217542	−	0.999763i	$-0.506925\pi$
$59$	−19.7175	−0.0435084	−0.0217542	+	0.999763i	$0.506925\pi$
$60$	−54.5748	−0.117426
$61$	−195.376	−0.410087	−0.205044	−	0.978753i	$-0.565734\pi$
$61$	−195.376	−0.410087	−0.205044	+	0.978753i	$0.565734\pi$
$62$	−500.063	−1.02432
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−112.961	−0.215556
$66$	163.778	0.305450
$67$	−511.263	−0.932250	−0.466125	−	0.884719i	$-0.654350\pi$
$67$	−511.263	−0.932250	−0.466125	+	0.884719i	$0.654350\pi$
$68$	462.692	0.825141
$69$	69.0000	0.120386
$70$	−63.6706	−0.108716
$71$	−68.8314	−0.115053	−0.0575267	−	0.998344i	$-0.518321\pi$
$71$	−68.8314	−0.115053	−0.0575267	+	0.998344i	$0.518321\pi$
$72$	72.0000	0.117851
$73$	904.894	1.45082	0.725410	−	0.688317i	$-0.241650\pi$
$73$	904.894	1.45082	0.725410	+	0.688317i	$0.241650\pi$
$74$	−86.9759	−0.136632
$75$	312.950	0.481818
$76$	−150.718	−0.227481
$77$	191.075	0.282792
$78$	149.029	0.216336
$79$	−188.251	−0.268100	−0.134050	−	0.990975i	$-0.542798\pi$
$79$	−188.251	−0.268100	−0.134050	+	0.990975i	$0.542798\pi$
$80$	72.7664	0.101694
$81$	81.0000	0.111111
$82$	−618.530	−0.832991
$83$	−1022.92	−1.35277	−0.676385	−	0.736548i	$-0.736455\pi$
$83$	−1022.92	−1.35277	−0.676385	+	0.736548i	$0.736455\pi$
$84$	84.0000	0.109109
$85$	526.069	0.671296
$86$	−127.175	−0.159461
$87$	−439.298	−0.541353
$88$	−218.371	−0.264527
$89$	1057.12	1.25904	0.629520	−	0.776984i	$-0.283252\pi$
$89$	1057.12	1.25904	0.629520	+	0.776984i	$0.283252\pi$
$90$	81.8622	0.0958782
$91$	173.867	0.200288
$92$	−92.0000	−0.104257
$93$	750.095	0.836357
$94$	−118.671	−0.130213
$95$	−171.363	−0.185068
$96$	−96.0000	−0.102062
$97$	−1744.68	−1.82624	−0.913122	−	0.407687i	$-0.866336\pi$
$97$	−1744.68	−1.82624	−0.913122	+	0.407687i	$0.866336\pi$
$98$	98.0000	0.101015
$99$	−245.667	−0.249399
$100$	−417.266	−0.417266
$101$	−191.243	−0.188410	−0.0942049	−	0.995553i	$-0.530031\pi$
$101$	−191.243	−0.188410	−0.0942049	+	0.995553i	$0.530031\pi$
$102$	−694.037	−0.673725
$103$	−870.057	−0.832323	−0.416162	−	0.909291i	$-0.636625\pi$
$103$	−870.057	−0.832323	−0.416162	+	0.909291i	$0.636625\pi$
$104$	−198.705	−0.187352
$105$	95.5059	0.0887659
$106$	−335.393	−0.307323
$107$	−669.770	−0.605132	−0.302566	−	0.953128i	$-0.597843\pi$
$107$	−669.770	−0.605132	−0.302566	+	0.953128i	$0.597843\pi$
$108$	−108.000	−0.0962250
$109$	−790.164	−0.694348	−0.347174	−	0.937801i	$-0.612859\pi$
$109$	−790.164	−0.694348	−0.347174	+	0.937801i	$0.612859\pi$
$110$	−248.282	−0.215207
$111$	130.464	0.111559
$112$	−112.000	−0.0944911
$113$	−708.736	−0.590020	−0.295010	−	0.955494i	$-0.595323\pi$
$113$	−708.736	−0.590020	−0.295010	+	0.955494i	$0.595323\pi$
$114$	226.077	0.185738
$115$	−104.602	−0.0848188
$116$	585.731	0.468825
$117$	−223.543	−0.176637
$118$	−39.4350	−0.0307651
$119$	−809.710	−0.623748
$120$	−109.150	−0.0830329
$121$	−585.909	−0.440202
$122$	−390.752	−0.289976
$123$	927.795	0.680134
$124$	−1000.13	−0.724306
$125$	−1042.91	−0.746245
$126$	−126.000	−0.0890871
$127$	−1814.01	−1.26746	−0.633730	−	0.773554i	$-0.718477\pi$
$127$	−1814.01	−1.26746	−0.633730	+	0.773554i	$0.718477\pi$
$128$	128.000	0.0883883
$129$	190.763	0.130199
$130$	−225.923	−0.152421
$131$	737.457	0.491847	0.245923	−	0.969289i	$-0.420909\pi$
$131$	737.457	0.491847	0.245923	+	0.969289i	$0.420909\pi$
$132$	327.556	0.215986
$133$	263.757	0.171960
$134$	−1022.53	−0.659200
$135$	−122.793	−0.0782842
$136$	925.383	0.583463
$137$	−979.388	−0.610765	−0.305382	−	0.952230i	$-0.598784\pi$
$137$	−979.388	−0.610765	−0.305382	+	0.952230i	$0.598784\pi$
$138$	138.000	0.0851257
$139$	1726.62	1.05360	0.526799	−	0.849990i	$-0.323392\pi$
$139$	1726.62	1.05360	0.526799	+	0.849990i	$0.323392\pi$
$140$	−127.341	−0.0768736
$141$	178.007	0.106318
$142$	−137.663	−0.0813550
$143$	677.990	0.396478
$144$	144.000	0.0833333
$145$	665.961	0.381414
$146$	1809.79	1.02588
$147$	−147.000	−0.0824786
$148$	−173.952	−0.0966132
$149$	−1043.88	−0.573944	−0.286972	−	0.957939i	$-0.592649\pi$
$149$	−1043.88	−0.573944	−0.286972	+	0.957939i	$0.592649\pi$
$150$	625.900	0.340697
$151$	−1103.07	−0.594478	−0.297239	−	0.954803i	$-0.596066\pi$
$151$	−1103.07	−0.594478	−0.297239	+	0.954803i	$0.596066\pi$
$152$	−301.437	−0.160854
$153$	1041.06	0.550094
$154$	382.149	0.199964
$155$	−1137.12	−0.589262
$156$	298.057	0.152972
$157$	1998.77	1.01604	0.508022	−	0.861344i	$-0.330377\pi$
$157$	1998.77	1.01604	0.508022	+	0.861344i	$0.330377\pi$
$158$	−376.502	−0.189575
$159$	503.089	0.250928
$160$	145.533	0.0719086
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	−1715.53	−0.824362	−0.412181	−	0.911102i	$-0.635233\pi$
$163$	−1715.53	−0.824362	−0.412181	+	0.911102i	$0.635233\pi$
$164$	−1237.06	−0.589013
$165$	372.423	0.175716
$166$	−2045.84	−0.956553
$167$	1245.59	0.577165	0.288583	−	0.957455i	$-0.406816\pi$
$167$	1245.59	0.577165	0.288583	+	0.957455i	$0.406816\pi$
$168$	168.000	0.0771517
$169$	−1580.07	−0.719193
$170$	1052.14	0.474678
$171$	−339.116	−0.151654
$172$	−254.350	−0.112756
$173$	−3010.35	−1.32296	−0.661482	−	0.749961i	$-0.730072\pi$
$173$	−3010.35	−1.32296	−0.661482	+	0.749961i	$0.730072\pi$
$174$	−878.596	−0.382794
$175$	730.216	0.315424
$176$	−436.742	−0.187049
$177$	59.1524	0.0251196
$178$	2114.24	0.890276
$179$	1881.68	0.785719	0.392859	−	0.919599i	$-0.371486\pi$
$179$	1881.68	0.785719	0.392859	+	0.919599i	$0.371486\pi$
$180$	163.724	0.0677961
$181$	2172.89	0.892318	0.446159	−	0.894954i	$-0.352792\pi$
$181$	2172.89	0.892318	0.446159	+	0.894954i	$0.352792\pi$
$182$	347.734	0.141625
$183$	586.128	0.236764
$184$	−184.000	−0.0737210
$185$	−197.779	−0.0786000
$186$	1500.19	0.591394
$187$	−3157.45	−1.23474
$188$	−237.342	−0.0920742
$189$	189.000	0.0727393
$190$	−342.726	−0.130863
$191$	−1945.26	−0.736930	−0.368465	−	0.929642i	$-0.620117\pi$
$191$	−1945.26	−0.736930	−0.368465	+	0.929642i	$0.620117\pi$
$192$	−192.000	−0.0721688
$193$	292.857	0.109224	0.0546121	−	0.998508i	$-0.482608\pi$
$193$	292.857	0.109224	0.0546121	+	0.998508i	$0.482608\pi$
$194$	−3489.36	−1.29135
$195$	338.884	0.124451
$196$	196.000	0.0714286
$197$	797.752	0.288515	0.144258	−	0.989540i	$-0.453921\pi$
$197$	797.752	0.288515	0.144258	+	0.989540i	$0.453921\pi$
$198$	−491.335	−0.176352
$199$	−501.050	−0.178485	−0.0892425	−	0.996010i	$-0.528445\pi$
$199$	−501.050	−0.178485	−0.0892425	+	0.996010i	$0.528445\pi$
$200$	−834.533	−0.295052
$201$	1533.79	0.538235
$202$	−382.486	−0.133226
$203$	−1025.03	−0.354398
$204$	−1388.07	−0.476395
$205$	−1406.51	−0.479194
$206$	−1740.11	−0.588541
$207$	−207.000	−0.0695048
$208$	−397.410	−0.132478
$209$	1028.52	0.340401
$210$	191.012	0.0627670
$211$	−5059.42	−1.65073	−0.825367	−	0.564597i	$-0.809032\pi$
$211$	−5059.42	−1.65073	−0.825367	+	0.564597i	$0.809032\pi$
$212$	−670.786	−0.217310
$213$	206.494	0.0664261
$214$	−1339.54	−0.427893
$215$	−289.190	−0.0917330
$216$	−216.000	−0.0680414
$217$	1750.22	0.547524
$218$	−1580.33	−0.490978
$219$	−2714.68	−0.837631
$220$	−496.565	−0.152174
$221$	−2873.10	−0.874504
$222$	260.928	0.0788844
$223$	3703.66	1.11218	0.556088	−	0.831124i	$-0.312302\pi$
$223$	3703.66	1.11218	0.556088	+	0.831124i	$0.312302\pi$
$224$	−224.000	−0.0668153
$225$	−938.849	−0.278178
$226$	−1417.47	−0.417207
$227$	2024.55	0.591957	0.295979	−	0.955195i	$-0.404354\pi$
$227$	2024.55	0.591957	0.295979	+	0.955195i	$0.404354\pi$
$228$	452.155	0.131336
$229$	6237.50	1.79994	0.899968	−	0.435956i	$-0.143590\pi$
$229$	6237.50	1.79994	0.899968	+	0.435956i	$0.143590\pi$
$230$	−209.203	−0.0599759
$231$	−573.224	−0.163270
$232$	1171.46	0.331509
$233$	147.434	0.0414537	0.0207268	−	0.999785i	$-0.493402\pi$
$233$	147.434	0.0414537	0.0207268	+	0.999785i	$0.493402\pi$
$234$	−447.086	−0.124901
$235$	−269.852	−0.0749073
$236$	−78.8699	−0.0217542
$237$	564.752	0.154787
$238$	−1619.42	−0.441056
$239$	1885.22	0.510229	0.255115	−	0.966911i	$-0.417887\pi$
$239$	1885.22	0.510229	0.255115	+	0.966911i	$0.417887\pi$
$240$	−218.299	−0.0587131
$241$	2022.48	0.540579	0.270290	−	0.962779i	$-0.412881\pi$
$241$	2022.48	0.540579	0.270290	+	0.962779i	$0.412881\pi$
$242$	−1171.82	−0.311270
$243$	−243.000	−0.0641500
$244$	−781.504	−0.205044
$245$	222.847	0.0581109
$246$	1855.59	0.480927
$247$	935.890	0.241090
$248$	−2000.25	−0.512162
$249$	3068.76	0.781023
$250$	−2085.82	−0.527675
$251$	3491.27	0.877955	0.438978	−	0.898498i	$-0.355341\pi$
$251$	3491.27	0.877955	0.438978	+	0.898498i	$0.355341\pi$
$252$	−252.000	−0.0629941
$253$	627.816	0.156010
$254$	−3628.02	−0.896230
$255$	−1578.21	−0.387573
$256$	256.000	0.0625000
$257$	−7230.22	−1.75490	−0.877449	−	0.479669i	$-0.840757\pi$
$257$	−7230.22	−1.75490	−0.877449	+	0.479669i	$0.840757\pi$
$258$	381.526	0.0920649
$259$	304.416	0.0730327
$260$	−451.845	−0.107778
$261$	1317.89	0.312550
$262$	1474.91	0.347788
$263$	1708.21	0.400504	0.200252	−	0.979744i	$-0.435824\pi$
$263$	1708.21	0.400504	0.200252	+	0.979744i	$0.435824\pi$
$264$	655.113	0.152725
$265$	−762.667	−0.176793
$266$	527.514	0.121594
$267$	−3171.36	−0.726907
$268$	−2045.05	−0.466125
$269$	3455.43	0.783201	0.391601	−	0.920135i	$-0.371921\pi$
$269$	3455.43	0.783201	0.391601	+	0.920135i	$0.371921\pi$
$270$	−245.587	−0.0553553
$271$	4787.50	1.07314	0.536568	−	0.843857i	$-0.319721\pi$
$271$	4787.50	1.07314	0.536568	+	0.843857i	$0.319721\pi$
$272$	1850.77	0.412571
$273$	−521.600	−0.115636
$274$	−1958.78	−0.431876
$275$	2847.46	0.624395
$276$	276.000	0.0601929
$277$	4273.80	0.927033	0.463516	−	0.886088i	$-0.346588\pi$
$277$	4273.80	0.927033	0.463516	+	0.886088i	$0.346588\pi$
$278$	3453.24	0.745006
$279$	−2250.28	−0.482871
$280$	−254.682	−0.0543578
$281$	4838.72	1.02724	0.513619	−	0.858018i	$-0.328304\pi$
$281$	4838.72	1.02724	0.513619	+	0.858018i	$0.328304\pi$
$282$	356.013	0.0751783
$283$	5123.18	1.07612	0.538059	−	0.842907i	$-0.319158\pi$
$283$	5123.18	1.07612	0.538059	+	0.842907i	$0.319158\pi$
$284$	−275.326	−0.0575267
$285$	514.089	0.106849
$286$	1355.98	0.280352
$287$	2164.86	0.445252
$288$	288.000	0.0589256
$289$	8467.22	1.72343
$290$	1331.92	0.269701
$291$	5234.05	1.05438
$292$	3619.57	0.725410
$293$	−2852.49	−0.568752	−0.284376	−	0.958713i	$-0.591786\pi$
$293$	−2852.49	−0.568752	−0.284376	+	0.958713i	$0.591786\pi$
$294$	−294.000	−0.0583212
$295$	−89.6731	−0.0176982
$296$	−347.904	−0.0683159
$297$	737.002	0.143991
$298$	−2087.75	−0.405840
$299$	571.277	0.110494
$300$	1251.80	0.240909
$301$	445.113	0.0852355
$302$	−2206.13	−0.420360
$303$	573.729	0.108778
$304$	−602.873	−0.113741
$305$	−888.551	−0.166814
$306$	2082.11	0.388975
$307$	3199.61	0.594824	0.297412	−	0.954749i	$-0.403876\pi$
$307$	3199.61	0.594824	0.297412	+	0.954749i	$0.403876\pi$
$308$	764.298	0.141396
$309$	2610.17	0.480542
$310$	−2274.24	−0.416671
$311$	−6542.42	−1.19288	−0.596442	−	0.802656i	$-0.703419\pi$
$311$	−6542.42	−1.19288	−0.596442	+	0.802656i	$0.703419\pi$
$312$	596.115	0.108168
$313$	3300.01	0.595935	0.297967	−	0.954576i	$-0.403691\pi$
$313$	3300.01	0.595935	0.297967	+	0.954576i	$0.403691\pi$
$314$	3997.53	0.718452
$315$	−286.518	−0.0512490
$316$	−753.003	−0.134050
$317$	6618.56	1.17267	0.586334	−	0.810070i	$-0.300571\pi$
$317$	6618.56	1.17267	0.586334	+	0.810070i	$0.300571\pi$
$318$	1006.18	0.177433
$319$	−3997.08	−0.701547
$320$	291.066	0.0508471
$321$	2009.31	0.349373
$322$	322.000	0.0557278
$323$	−4358.50	−0.750816
$324$	324.000	0.0555556
$325$	2591.03	0.442229
$326$	−3431.07	−0.582912
$327$	2370.49	0.400882
$328$	−2474.12	−0.416495
$329$	415.349	0.0696016
$330$	744.847	0.124250
$331$	61.2146	0.0101651	0.00508257	−	0.999987i	$-0.498382\pi$
$331$	61.2146	0.0101651	0.00508257	+	0.999987i	$0.498382\pi$
$332$	−4091.68	−0.676385
$333$	−391.392	−0.0644088
$334$	2491.18	0.408117
$335$	−2325.17	−0.379217
$336$	336.000	0.0545545
$337$	−8172.78	−1.32107	−0.660533	−	0.750797i	$-0.729670\pi$
$337$	−8172.78	−1.32107	−0.660533	+	0.750797i	$0.729670\pi$
$338$	−3160.14	−0.508547
$339$	2126.21	0.340648
$340$	2104.28	0.335648
$341$	6824.95	1.08385
$342$	−678.232	−0.107236
$343$	−343.000	−0.0539949
$344$	−508.701	−0.0797305
$345$	313.805	0.0489701
$346$	−6020.70	−0.935477
$347$	5148.14	0.796445	0.398223	−	0.917289i	$-0.369627\pi$
$347$	5148.14	0.796445	0.398223	+	0.917289i	$0.369627\pi$
$348$	−1757.19	−0.270676
$349$	−5388.42	−0.826463	−0.413231	−	0.910626i	$-0.635600\pi$
$349$	−5388.42	−0.826463	−0.413231	+	0.910626i	$0.635600\pi$
$350$	1460.43	0.223038
$351$	670.629	0.101982
$352$	−873.484	−0.132264
$353$	6788.61	1.02357	0.511787	−	0.859113i	$-0.328984\pi$
$353$	6788.61	1.02357	0.511787	+	0.859113i	$0.328984\pi$
$354$	118.305	0.0177622
$355$	−313.039	−0.0468010
$356$	4228.48	0.629520
$357$	2429.13	0.360121
$358$	3763.37	0.555587
$359$	961.319	0.141327	0.0706636	−	0.997500i	$-0.477488\pi$
$359$	961.319	0.141327	0.0706636	+	0.997500i	$0.477488\pi$
$360$	327.449	0.0479391
$361$	−5439.25	−0.793009
$362$	4345.78	0.630964
$363$	1757.73	0.254151
$364$	695.467	0.100144
$365$	4115.37	0.590159
$366$	1172.26	0.167417
$367$	3404.43	0.484223	0.242111	−	0.970248i	$-0.422160\pi$
$367$	3404.43	0.484223	0.242111	+	0.970248i	$0.422160\pi$
$368$	−368.000	−0.0521286
$369$	−2783.39	−0.392676
$370$	−395.558	−0.0555786
$371$	1173.88	0.164271
$372$	3000.38	0.418178
$373$	3255.96	0.451976	0.225988	−	0.974130i	$-0.427439\pi$
$373$	3255.96	0.451976	0.225988	+	0.974130i	$0.427439\pi$
$374$	−6314.90	−0.873090
$375$	3128.73	0.430845
$376$	−474.684	−0.0651063
$377$	−3637.11	−0.496872
$378$	378.000	0.0514344
$379$	−4555.20	−0.617374	−0.308687	−	0.951164i	$-0.599890\pi$
$379$	−4555.20	−0.617374	−0.308687	+	0.951164i	$0.599890\pi$
$380$	−685.452	−0.0925340
$381$	5442.03	0.731768
$382$	−3890.51	−0.521089
$383$	−7991.36	−1.06616	−0.533080	−	0.846065i	$-0.678966\pi$
$383$	−7991.36	−1.06616	−0.533080	+	0.846065i	$0.678966\pi$
$384$	−384.000	−0.0510310
$385$	868.988	0.115033
$386$	585.713	0.0772332
$387$	−572.288	−0.0751707
$388$	−6978.73	−0.913122
$389$	6966.20	0.907971	0.453985	−	0.891009i	$-0.350002\pi$
$389$	6966.20	0.907971	0.453985	+	0.891009i	$0.350002\pi$
$390$	677.768	0.0880003
$391$	−2660.48	−0.344108
$392$	392.000	0.0505076
$393$	−2212.37	−0.283968
$394$	1595.50	0.204011
$395$	−856.146	−0.109057
$396$	−982.669	−0.124699
$397$	715.627	0.0904692	0.0452346	−	0.998976i	$-0.485596\pi$
$397$	715.627	0.0904692	0.0452346	+	0.998976i	$0.485596\pi$
$398$	−1002.10	−0.126208
$399$	−791.271	−0.0992809
$400$	−1669.07	−0.208633
$401$	−5070.01	−0.631383	−0.315691	−	0.948862i	$-0.602236\pi$
$401$	−5070.01	−0.631383	−0.315691	+	0.948862i	$0.602236\pi$
$402$	3067.58	0.380589
$403$	6210.31	0.767637
$404$	−764.972	−0.0942049
$405$	368.380	0.0451974
$406$	−2050.06	−0.250598
$407$	1187.06	0.144571
$408$	−2776.15	−0.336862
$409$	7344.41	0.887916	0.443958	−	0.896047i	$-0.353574\pi$
$409$	7344.41	0.887916	0.443958	+	0.896047i	$0.353574\pi$
$410$	−2813.01	−0.338841
$411$	2938.16	0.352625
$412$	−3480.23	−0.416162
$413$	138.022	0.0164446
$414$	−414.000	−0.0491473
$415$	−4652.14	−0.550276
$416$	−794.820	−0.0936761
$417$	−5179.86	−0.608295
$418$	2057.03	0.240700
$419$	11047.6	1.28809	0.644047	−	0.764986i	$-0.277254\pi$
$419$	11047.6	1.28809	0.644047	+	0.764986i	$0.277254\pi$
$420$	382.024	0.0443830
$421$	6407.15	0.741723	0.370861	−	0.928688i	$-0.379062\pi$
$421$	6407.15	0.741723	0.370861	+	0.928688i	$0.379062\pi$
$422$	−10118.8	−1.16725
$423$	−534.020	−0.0613828
$424$	−1341.57	−0.153662
$425$	−12066.6	−1.37721
$426$	412.989	0.0469703
$427$	1367.63	0.154998
$428$	−2679.08	−0.302566
$429$	−2033.97	−0.228907
$430$	−578.380	−0.0648650
$431$	−4646.93	−0.519338	−0.259669	−	0.965698i	$-0.583613\pi$
$431$	−4646.93	−0.519338	−0.259669	+	0.965698i	$0.583613\pi$
$432$	−432.000	−0.0481125
$433$	9415.72	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$433$	9415.72	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$434$	3500.44	0.387158
$435$	−1997.88	−0.220210
$436$	−3160.65	−0.347174
$437$	866.630	0.0948662
$438$	−5429.36	−0.592294
$439$	−2171.74	−0.236108	−0.118054	−	0.993007i	$-0.537666\pi$
$439$	−2171.74	−0.236108	−0.118054	+	0.993007i	$0.537666\pi$
$440$	−993.129	−0.107604
$441$	441.000	0.0476190
$442$	−5746.19	−0.618368
$443$	−13706.0	−1.46996	−0.734978	−	0.678091i	$-0.762808\pi$
$443$	−13706.0	−1.46996	−0.734978	+	0.678091i	$0.762808\pi$
$444$	521.856	0.0557797
$445$	4807.68	0.512148
$446$	7407.31	0.786427
$447$	3131.63	0.331367
$448$	−448.000	−0.0472456
$449$	−3668.89	−0.385625	−0.192813	−	0.981236i	$-0.561761\pi$
$449$	−3668.89	−0.385625	−0.192813	+	0.981236i	$0.561761\pi$
$450$	−1877.70	−0.196701
$451$	8441.81	0.881396
$452$	−2834.95	−0.295010
$453$	3309.20	0.343222
$454$	4049.11	0.418577
$455$	790.729	0.0814724
$456$	904.310	0.0928688
$457$	−3371.01	−0.345053	−0.172526	−	0.985005i	$-0.555193\pi$
$457$	−3371.01	−0.345053	−0.172526	+	0.985005i	$0.555193\pi$
$458$	12475.0	1.27275
$459$	−3123.17	−0.317597
$460$	−418.407	−0.0424094
$461$	−1032.02	−0.104265	−0.0521325	−	0.998640i	$-0.516602\pi$
$461$	−1032.02	−0.104265	−0.0521325	+	0.998640i	$0.516602\pi$
$462$	−1146.45	−0.115449
$463$	7838.26	0.786771	0.393385	−	0.919374i	$-0.371304\pi$
$463$	7838.26	0.786771	0.393385	+	0.919374i	$0.371304\pi$
$464$	2342.92	0.234413
$465$	3411.36	0.340210
$466$	294.868	0.0293122
$467$	−11523.8	−1.14188	−0.570941	−	0.820991i	$-0.693421\pi$
$467$	−11523.8	−1.14188	−0.570941	+	0.820991i	$0.693421\pi$
$468$	−894.172	−0.0883186
$469$	3578.84	0.352357
$470$	−539.704	−0.0529675
$471$	−5996.30	−0.586613
$472$	−157.740	−0.0153826
$473$	1735.71	0.168727
$474$	1129.50	0.109451
$475$	3930.60	0.379681
$476$	−3238.84	−0.311874
$477$	−1509.27	−0.144873
$478$	3770.44	0.360787
$479$	−6230.77	−0.594345	−0.297172	−	0.954824i	$-0.596044\pi$
$479$	−6230.77	−0.594345	−0.297172	+	0.954824i	$0.596044\pi$
$480$	−436.598	−0.0415165
$481$	1080.16	0.102393
$482$	4044.97	0.382247
$483$	−483.000	−0.0455016
$484$	−2343.63	−0.220101
$485$	−7934.64	−0.742873
$486$	−486.000	−0.0453609
$487$	8776.81	0.816664	0.408332	−	0.912833i	$-0.366111\pi$
$487$	8776.81	0.816664	0.408332	+	0.912833i	$0.366111\pi$
$488$	−1563.01	−0.144988
$489$	5146.60	0.475946
$490$	445.694	0.0410906
$491$	−10900.2	−1.00187	−0.500937	−	0.865483i	$-0.667011\pi$
$491$	−10900.2	−1.00187	−0.500937	+	0.865483i	$0.667011\pi$
$492$	3711.18	0.340067
$493$	16938.3	1.54739
$494$	1871.78	0.170476
$495$	−1117.27	−0.101450
$496$	−4000.50	−0.362153
$497$	481.820	0.0434861
$498$	6137.52	0.552266
$499$	−2959.50	−0.265502	−0.132751	−	0.991149i	$-0.542381\pi$
$499$	−2959.50	−0.265502	−0.132751	+	0.991149i	$0.542381\pi$
$500$	−4171.64	−0.373123
$501$	−3736.77	−0.333227
$502$	6982.53	0.620808
$503$	8422.33	0.746587	0.373294	−	0.927713i	$-0.378228\pi$
$503$	8422.33	0.746587	0.373294	+	0.927713i	$0.378228\pi$
$504$	−504.000	−0.0445435
$505$	−869.754	−0.0766407
$506$	1255.63	0.110316
$507$	4740.20	0.415227
$508$	−7256.04	−0.633730
$509$	−8782.66	−0.764803	−0.382401	−	0.923996i	$-0.624903\pi$
$509$	−8782.66	−0.764803	−0.382401	+	0.923996i	$0.624903\pi$
$510$	−3156.41	−0.274056
$511$	−6334.26	−0.548358
$512$	512.000	0.0441942
$513$	1017.35	0.0875576
$514$	−14460.4	−1.24090
$515$	−3956.93	−0.338570
$516$	763.051	0.0650997
$517$	1619.64	0.137779
$518$	608.832	0.0516419
$519$	9031.05	0.763814
$520$	−903.690	−0.0762105
$521$	−677.201	−0.0569457	−0.0284728	−	0.999595i	$-0.509064\pi$
$521$	−677.201	−0.0569457	−0.0284728	+	0.999595i	$0.509064\pi$
$522$	2635.79	0.221006
$523$	5280.06	0.441455	0.220727	−	0.975336i	$-0.429157\pi$
$523$	5280.06	0.441455	0.220727	+	0.975336i	$0.429157\pi$
$524$	2949.83	0.245923
$525$	−2190.65	−0.182110
$526$	3416.41	0.283199
$527$	−28921.9	−2.39062
$528$	1310.23	0.107993
$529$	529.000	0.0434783
$530$	−1525.33	−0.125012
$531$	−177.457	−0.0145028
$532$	1055.03	0.0859798
$533$	7681.56	0.624250
$534$	−6342.73	−0.514001
$535$	−3046.05	−0.246153
$536$	−4090.10	−0.329600
$537$	−5645.05	−0.453635
$538$	6910.86	0.553807
$539$	−1337.52	−0.106885
$540$	−491.173	−0.0391421
$541$	14279.4	1.13479	0.567393	−	0.823447i	$-0.307952\pi$
$541$	14279.4	1.13479	0.567393	+	0.823447i	$0.307952\pi$
$542$	9574.99	0.758821
$543$	−6518.67	−0.515180
$544$	3701.53	0.291731
$545$	−3593.59	−0.282445
$546$	−1043.20	−0.0817672
$547$	17320.6	1.35388	0.676941	−	0.736037i	$-0.263305\pi$
$547$	17320.6	1.35388	0.676941	+	0.736037i	$0.263305\pi$
$548$	−3917.55	−0.305382
$549$	−1758.38	−0.136696
$550$	5694.93	0.441514
$551$	−5517.52	−0.426596
$552$	552.000	0.0425628
$553$	1317.76	0.101332
$554$	8547.61	0.655511
$555$	593.337	0.0453797
$556$	6906.48	0.526799
$557$	−6074.49	−0.462091	−0.231045	−	0.972943i	$-0.574215\pi$
$557$	−6074.49	−0.462091	−0.231045	+	0.972943i	$0.574215\pi$
$558$	−4500.57	−0.341441
$559$	1579.40	0.119502
$560$	−509.365	−0.0384368
$561$	9472.35	0.712875
$562$	9677.45	0.726368
$563$	13669.3	1.02326	0.511628	−	0.859207i	$-0.329042\pi$
$563$	13669.3	1.02326	0.511628	+	0.859207i	$0.329042\pi$
$564$	712.026	0.0531591
$565$	−3223.26	−0.240006
$566$	10246.4	0.760930
$567$	−567.000	−0.0419961
$568$	−550.652	−0.0406775
$569$	−10244.1	−0.754753	−0.377377	−	0.926060i	$-0.623174\pi$
$569$	−10244.1	−0.754753	−0.377377	+	0.926060i	$0.623174\pi$
$570$	1028.18	0.0755537
$571$	−16023.6	−1.17437	−0.587187	−	0.809451i	$-0.699765\pi$
$571$	−16023.6	−1.17437	−0.587187	+	0.809451i	$0.699765\pi$
$572$	2711.96	0.198239
$573$	5835.77	0.425467
$574$	4329.71	0.314841
$575$	2399.28	0.174012
$576$	576.000	0.0416667
$577$	3369.93	0.243140	0.121570	−	0.992583i	$-0.461207\pi$
$577$	3369.93	0.243140	0.121570	+	0.992583i	$0.461207\pi$
$578$	16934.4	1.21865
$579$	−878.570	−0.0630607
$580$	2663.84	0.190707
$581$	7160.44	0.511299
$582$	10468.1	0.745561
$583$	4577.50	0.325182
$584$	7239.15	0.512942
$585$	−1016.65	−0.0718519
$586$	−5704.98	−0.402168
$587$	−27867.8	−1.95950	−0.979752	−	0.200213i	$-0.935836\pi$
$587$	−27867.8	−1.95950	−0.979752	+	0.200213i	$0.935836\pi$
$588$	−588.000	−0.0412393
$589$	9421.08	0.659064
$590$	−179.346	−0.0125145
$591$	−2393.26	−0.166574
$592$	−695.807	−0.0483066
$593$	16468.7	1.14045	0.570226	−	0.821488i	$-0.306856\pi$
$593$	16468.7	1.14045	0.570226	+	0.821488i	$0.306856\pi$
$594$	1474.00	0.101817
$595$	−3682.48	−0.253726
$596$	−4175.51	−0.286972
$597$	1503.15	0.103048
$598$	1142.55	0.0781312
$599$	−7009.58	−0.478137	−0.239068	−	0.971003i	$-0.576842\pi$
$599$	−7009.58	−0.478137	−0.239068	+	0.971003i	$0.576842\pi$
$600$	2503.60	0.170348
$601$	−13039.5	−0.885011	−0.442505	−	0.896766i	$-0.645910\pi$
$601$	−13039.5	−0.885011	−0.442505	+	0.896766i	$0.645910\pi$
$602$	890.226	0.0602706
$603$	−4601.37	−0.310750
$604$	−4412.26	−0.297239
$605$	−2664.65	−0.179064
$606$	1147.46	0.0769180
$607$	−4177.64	−0.279350	−0.139675	−	0.990197i	$-0.544606\pi$
$607$	−4177.64	−0.279350	−0.139675	+	0.990197i	$0.544606\pi$
$608$	−1205.75	−0.0804268
$609$	3075.09	0.204612
$610$	−1777.10	−0.117955
$611$	1473.78	0.0975825
$612$	4164.22	0.275047
$613$	22187.1	1.46187	0.730936	−	0.682446i	$-0.239084\pi$
$613$	22187.1	1.46187	0.730936	+	0.682446i	$0.239084\pi$
$614$	6399.21	0.420604
$615$	4219.52	0.276663
$616$	1528.60	0.0999820
$617$	1913.60	0.124860	0.0624302	−	0.998049i	$-0.480115\pi$
$617$	1913.60	0.124860	0.0624302	+	0.998049i	$0.480115\pi$
$618$	5220.34	0.339795
$619$	22856.0	1.48410	0.742051	−	0.670344i	$-0.233853\pi$
$619$	22856.0	1.48410	0.742051	+	0.670344i	$0.233853\pi$
$620$	−4548.47	−0.294631
$621$	621.000	0.0401286
$622$	−13084.8	−0.843496
$623$	−7399.85	−0.475873
$624$	1192.23	0.0764862
$625$	8296.53	0.530978
$626$	6600.02	0.421389
$627$	−3085.55	−0.196531
$628$	7995.07	0.508022
$629$	−5030.38	−0.318878
$630$	−573.035	−0.0362385
$631$	9033.49	0.569917	0.284958	−	0.958540i	$-0.408020\pi$
$631$	9033.49	0.569917	0.284958	+	0.958540i	$0.408020\pi$
$632$	−1506.01	−0.0947875
$633$	15178.3	0.953052
$634$	13237.1	0.829201
$635$	−8249.94	−0.515573
$636$	2012.36	0.125464
$637$	−1217.07	−0.0757017
$638$	−7994.16	−0.496069
$639$	−619.483	−0.0383511
$640$	582.131	0.0359543
$641$	−5558.97	−0.342537	−0.171268	−	0.985224i	$-0.554786\pi$
$641$	−5558.97	−0.342537	−0.171268	+	0.985224i	$0.554786\pi$
$642$	4018.62	0.247044
$643$	25732.1	1.57819	0.789094	−	0.614273i	$-0.210551\pi$
$643$	25732.1	1.57819	0.789094	+	0.614273i	$0.210551\pi$
$644$	644.000	0.0394055
$645$	867.570	0.0529621
$646$	−8717.01	−0.530907
$647$	4644.87	0.282239	0.141120	−	0.989993i	$-0.454930\pi$
$647$	4644.87	0.282239	0.141120	+	0.989993i	$0.454930\pi$
$648$	648.000	0.0392837
$649$	538.215	0.0325529
$650$	5182.06	0.312703
$651$	−5250.66	−0.316113
$652$	−6862.14	−0.412181
$653$	−27415.9	−1.64298	−0.821492	−	0.570220i	$-0.806858\pi$
$653$	−27415.9	−1.64298	−0.821492	+	0.570220i	$0.806858\pi$
$654$	4740.98	0.283466
$655$	3353.88	0.200072
$656$	−4948.24	−0.294507
$657$	8144.04	0.483606
$658$	830.698	0.0492157
$659$	13914.7	0.822519	0.411260	−	0.911518i	$-0.365089\pi$
$659$	13914.7	0.822519	0.411260	+	0.911518i	$0.365089\pi$
$660$	1489.69	0.0878580
$661$	−30494.1	−1.79438	−0.897188	−	0.441650i	$-0.854393\pi$
$661$	−30494.1	−1.79438	−0.897188	+	0.441650i	$0.854393\pi$
$662$	122.429	0.00718784
$663$	8619.29	0.504895
$664$	−8183.35	−0.478277
$665$	1199.54	0.0699492
$666$	−782.783	−0.0455439
$667$	−3367.95	−0.195514
$668$	4982.36	0.288583
$669$	−11111.0	−0.642115
$670$	−4650.35	−0.268147
$671$	5333.05	0.306826
$672$	672.000	0.0385758
$673$	3757.91	0.215241	0.107620	−	0.994192i	$-0.465677\pi$
$673$	3757.91	0.215241	0.107620	+	0.994192i	$0.465677\pi$
$674$	−16345.6	−0.934135
$675$	2816.55	0.160606
$676$	−6320.27	−0.359597
$677$	10918.7	0.619850	0.309925	−	0.950761i	$-0.399696\pi$
$677$	10918.7	0.619850	0.309925	+	0.950761i	$0.399696\pi$
$678$	4252.42	0.240875
$679$	12212.8	0.690255
$680$	4208.55	0.237339
$681$	−6073.66	−0.341767
$682$	13649.9	0.766396
$683$	−19198.4	−1.07556	−0.537780	−	0.843085i	$-0.680737\pi$
$683$	−19198.4	−1.07556	−0.537780	+	0.843085i	$0.680737\pi$
$684$	−1356.46	−0.0758271
$685$	−4454.16	−0.248445
$686$	−686.000	−0.0381802
$687$	−18712.5	−1.03919
$688$	−1017.40	−0.0563780
$689$	4165.26	0.230311
$690$	627.610	0.0346271
$691$	−1049.30	−0.0577673	−0.0288837	−	0.999583i	$-0.509195\pi$
$691$	−1049.30	−0.0577673	−0.0288837	+	0.999583i	$0.509195\pi$
$692$	−12041.4	−0.661482
$693$	1719.67	0.0942639
$694$	10296.3	0.563172
$695$	7852.50	0.428579
$696$	−3514.38	−0.191397
$697$	−35773.6	−1.94408
$698$	−10776.8	−0.584397
$699$	−442.301	−0.0239333
$700$	2920.86	0.157712
$701$	−18076.9	−0.973976	−0.486988	−	0.873409i	$-0.661904\pi$
$701$	−18076.9	−0.973976	−0.486988	+	0.873409i	$0.661904\pi$
$702$	1341.26	0.0721119
$703$	1638.61	0.0879108
$704$	−1746.97	−0.0935246
$705$	809.556	0.0432477
$706$	13577.2	0.723776
$707$	1338.70	0.0712122
$708$	236.610	0.0125598
$709$	−18589.8	−0.984704	−0.492352	−	0.870396i	$-0.663863\pi$
$709$	−18589.8	−0.984704	−0.492352	+	0.870396i	$0.663863\pi$
$710$	−626.077	−0.0330933
$711$	−1694.26	−0.0893665
$712$	8456.97	0.445138
$713$	5750.72	0.302057
$714$	4858.26	0.254644
$715$	3083.43	0.161278
$716$	7526.73	0.392859
$717$	−5655.66	−0.294581
$718$	1922.64	0.0999334
$719$	−32219.9	−1.67121	−0.835606	−	0.549330i	$-0.814883\pi$
$719$	−32219.9	−1.67121	−0.835606	+	0.549330i	$0.814883\pi$
$720$	654.898	0.0338981
$721$	6090.40	0.314589
$722$	−10878.5	−0.560742
$723$	−6067.45	−0.312104
$724$	8691.56	0.446159
$725$	−15275.4	−0.782500
$726$	3515.45	0.179712
$727$	917.575	0.0468101	0.0234051	−	0.999726i	$-0.492549\pi$
$727$	917.575	0.0468101	0.0234051	+	0.999726i	$0.492549\pi$
$728$	1390.93	0.0708124
$729$	729.000	0.0370370
$730$	8230.73	0.417306
$731$	−7355.36	−0.372159
$732$	2344.51	0.118382
$733$	5046.72	0.254304	0.127152	−	0.991883i	$-0.459416\pi$
$733$	5046.72	0.254304	0.127152	+	0.991883i	$0.459416\pi$
$734$	6808.86	0.342397
$735$	−668.541	−0.0335504
$736$	−736.000	−0.0368605
$737$	13955.6	0.697506
$738$	−5566.77	−0.277664
$739$	16919.5	0.842212	0.421106	−	0.907011i	$-0.361642\pi$
$739$	16919.5	0.842212	0.421106	+	0.907011i	$0.361642\pi$
$740$	−791.116	−0.0393000
$741$	−2807.67	−0.139193
$742$	2347.75	0.116157
$743$	31602.3	1.56040	0.780199	−	0.625532i	$-0.215118\pi$
$743$	31602.3	1.56040	0.780199	+	0.625532i	$0.215118\pi$
$744$	6000.76	0.295697
$745$	−4747.45	−0.233467
$746$	6511.92	0.319596
$747$	−9206.27	−0.450924
$748$	−12629.8	−0.617368
$749$	4688.39	0.228718
$750$	6257.45	0.304653
$751$	−37113.3	−1.80331	−0.901654	−	0.432458i	$-0.857646\pi$
$751$	−37113.3	−1.80331	−0.901654	+	0.432458i	$0.857646\pi$
$752$	−949.369	−0.0460371
$753$	−10473.8	−0.506888
$754$	−7274.22	−0.351342
$755$	−5016.63	−0.241820
$756$	756.000	0.0363696
$757$	26184.6	1.25719	0.628597	−	0.777731i	$-0.283629\pi$
$757$	26184.6	1.25719	0.628597	+	0.777731i	$0.283629\pi$
$758$	−9110.39	−0.436549
$759$	−1883.45	−0.0900723
$760$	−1370.90	−0.0654314
$761$	26555.9	1.26498	0.632492	−	0.774567i	$-0.282032\pi$
$761$	26555.9	1.26498	0.632492	+	0.774567i	$0.282032\pi$
$762$	10884.1	0.517438
$763$	5531.15	0.262439
$764$	−7781.02	−0.368465
$765$	4734.62	0.223765
$766$	−15982.7	−0.753890
$767$	489.745	0.0230556
$768$	−768.000	−0.0360844
$769$	26040.8	1.22114	0.610570	−	0.791962i	$-0.290940\pi$
$769$	26040.8	1.22114	0.610570	+	0.791962i	$0.290940\pi$
$770$	1737.98	0.0813407
$771$	21690.7	1.01319
$772$	1171.43	0.0546121
$773$	−36557.3	−1.70100	−0.850501	−	0.525973i	$-0.823701\pi$
$773$	−36557.3	−1.70100	−0.850501	+	0.525973i	$0.823701\pi$
$774$	−1144.58	−0.0531537
$775$	26082.4	1.20891
$776$	−13957.5	−0.645675
$777$	−913.247	−0.0421655
$778$	13932.4	0.642032
$779$	11653.0	0.535958
$780$	1355.54	0.0622256
$781$	1878.85	0.0860825
$782$	−5320.95	−0.243321
$783$	−3953.68	−0.180451
$784$	784.000	0.0357143
$785$	9090.19	0.413303
$786$	−4424.74	−0.200796
$787$	25486.3	1.15437	0.577184	−	0.816614i	$-0.304152\pi$
$787$	25486.3	1.15437	0.577184	+	0.816614i	$0.304152\pi$
$788$	3191.01	0.144258
$789$	−5124.62	−0.231231
$790$	−1712.29	−0.0771147
$791$	4961.15	0.223007
$792$	−1965.34	−0.0881758
$793$	4852.77	0.217310
$794$	1431.25	0.0639714
$795$	2288.00	0.102072
$796$	−2004.20	−0.0892425
$797$	26667.7	1.18522	0.592608	−	0.805491i	$-0.298098\pi$
$797$	26667.7	1.18522	0.592608	+	0.805491i	$0.298098\pi$
$798$	−1582.54	−0.0702022
$799$	−6863.51	−0.303897
$800$	−3338.13	−0.147526
$801$	9514.09	0.419680
$802$	−10140.0	−0.446455
$803$	−24700.3	−1.08550
$804$	6135.16	0.269117
$805$	732.212	0.0320585
$806$	12420.6	0.542801
$807$	−10366.3	−0.452182
$808$	−1529.94	−0.0666129
$809$	−4150.69	−0.180384	−0.0901920	−	0.995924i	$-0.528748\pi$
$809$	−4150.69	−0.180384	−0.0901920	+	0.995924i	$0.528748\pi$
$810$	736.760	0.0319594
$811$	−36435.4	−1.57758	−0.788791	−	0.614661i	$-0.789293\pi$
$811$	−36435.4	−1.57758	−0.788791	+	0.614661i	$0.789293\pi$
$812$	−4100.11	−0.177199
$813$	−14362.5	−0.619575
$814$	2374.13	0.102227
$815$	−7802.08	−0.335331
$816$	−5552.30	−0.238198
$817$	2395.95	0.102600
$818$	14688.8	0.627852
$819$	1564.80	0.0667626
$820$	−5626.03	−0.239597
$821$	3238.29	0.137658	0.0688289	−	0.997628i	$-0.478074\pi$
$821$	3238.29	0.137658	0.0688289	+	0.997628i	$0.478074\pi$
$822$	5876.33	0.249344
$823$	−37044.6	−1.56901	−0.784503	−	0.620124i	$-0.787082\pi$
$823$	−37044.6	−1.56901	−0.784503	+	0.620124i	$0.787082\pi$
$824$	−6960.46	−0.294271
$825$	−8542.39	−0.360494
$826$	276.045	0.0116281
$827$	−18120.4	−0.761921	−0.380961	−	0.924591i	$-0.624407\pi$
$827$	−18120.4	−0.761921	−0.380961	+	0.924591i	$0.624407\pi$
$828$	−828.000	−0.0347524
$829$	−3208.70	−0.134430	−0.0672152	−	0.997738i	$-0.521411\pi$
$829$	−3208.70	−0.134430	−0.0672152	+	0.997738i	$0.521411\pi$
$830$	−9304.27	−0.389104
$831$	−12821.4	−0.535223
$832$	−1589.64	−0.0662390
$833$	5667.97	0.235755
$834$	−10359.7	−0.430129
$835$	5664.82	0.234777
$836$	4114.06	0.170201
$837$	6750.85	0.278786
$838$	22095.2	0.910820
$839$	−12643.6	−0.520268	−0.260134	−	0.965572i	$-0.583767\pi$
$839$	−12643.6	−0.520268	−0.260134	+	0.965572i	$0.583767\pi$
$840$	764.047	0.0313835
$841$	−2946.48	−0.120812
$842$	12814.3	0.524477
$843$	−14516.2	−0.593077
$844$	−20237.7	−0.825367
$845$	−7185.99	−0.292551
$846$	−1068.04	−0.0434042
$847$	4101.36	0.166381
$848$	−2683.14	−0.108655
$849$	−15369.5	−0.621297
$850$	−24133.2	−0.973838
$851$	1000.22	0.0402905
$852$	825.977	0.0332130
$853$	−1849.26	−0.0742290	−0.0371145	−	0.999311i	$-0.511817\pi$
$853$	−1849.26	−0.0742290	−0.0371145	+	0.999311i	$0.511817\pi$
$854$	2735.26	0.109600
$855$	−1542.27	−0.0616894
$856$	−5358.16	−0.213946
$857$	43436.3	1.73134	0.865669	−	0.500617i	$-0.166893\pi$
$857$	43436.3	1.73134	0.865669	+	0.500617i	$0.166893\pi$
$858$	−4067.94	−0.161862
$859$	−42401.9	−1.68421	−0.842104	−	0.539315i	$-0.818683\pi$
$859$	−42401.9	−1.68421	−0.842104	+	0.539315i	$0.818683\pi$
$860$	−1156.76	−0.0458665
$861$	−6494.57	−0.257066
$862$	−9293.86	−0.367228
$863$	14338.3	0.565563	0.282781	−	0.959184i	$-0.408743\pi$
$863$	14338.3	0.565563	0.282781	+	0.959184i	$0.408743\pi$
$864$	−864.000	−0.0340207
$865$	−13690.8	−0.538151
$866$	18831.4	0.738936
$867$	−25401.7	−0.995024
$868$	7000.88	0.273762
$869$	5138.56	0.200591
$870$	−3995.77	−0.155712
$871$	12698.8	0.494010
$872$	−6321.31	−0.245489
$873$	−15702.1	−0.608748
$874$	1733.26	0.0670806
$875$	7300.36	0.282054
$876$	−10858.7	−0.418815
$877$	−8856.74	−0.341016	−0.170508	−	0.985356i	$-0.554541\pi$
$877$	−8856.74	−0.341016	−0.170508	+	0.985356i	$0.554541\pi$
$878$	−4343.47	−0.166953
$879$	8557.47	0.328369
$880$	−1986.26	−0.0760872
$881$	−43066.5	−1.64693	−0.823466	−	0.567365i	$-0.807963\pi$
$881$	−43066.5	−1.64693	−0.823466	+	0.567365i	$0.807963\pi$
$882$	882.000	0.0336718
$883$	−1518.56	−0.0578750	−0.0289375	−	0.999581i	$-0.509212\pi$
$883$	−1518.56	−0.0578750	−0.0289375	+	0.999581i	$0.509212\pi$
$884$	−11492.4	−0.437252
$885$	269.019	0.0102181
$886$	−27412.0	−1.03942
$887$	−38164.6	−1.44469	−0.722346	−	0.691531i	$-0.756936\pi$
$887$	−38164.6	−1.44469	−0.722346	+	0.691531i	$0.756936\pi$
$888$	1043.71	0.0394422
$889$	12698.1	0.479055
$890$	9615.36	0.362143
$891$	−2211.01	−0.0831330
$892$	14814.6	0.556088
$893$	2235.74	0.0837806
$894$	6263.26	0.234312
$895$	8557.71	0.319612
$896$	−896.000	−0.0334077
$897$	−1713.83	−0.0637939
$898$	−7337.78	−0.272678
$899$	−36612.8	−1.35829
$900$	−3755.40	−0.139089
$901$	−19397.9	−0.717246
$902$	16883.6	0.623241
$903$	−1335.34	−0.0492108
$904$	−5669.89	−0.208604
$905$	9882.08	0.362974
$906$	6618.39	0.242695
$907$	−43627.2	−1.59715	−0.798576	−	0.601894i	$-0.794413\pi$
$907$	−43627.2	−1.59715	−0.798576	+	0.601894i	$0.794413\pi$
$908$	8098.21	0.295979
$909$	−1721.19	−0.0628033
$910$	1581.46	0.0576097
$911$	19899.3	0.723702	0.361851	−	0.932236i	$-0.382145\pi$
$911$	19899.3	0.723702	0.361851	+	0.932236i	$0.382145\pi$
$912$	1808.62	0.0656682
$913$	27922.0	1.01214
$914$	−6742.02	−0.243989
$915$	2665.65	0.0963101
$916$	24950.0	0.899968
$917$	−5162.20	−0.185901
$918$	−6246.34	−0.224575
$919$	−6572.58	−0.235919	−0.117959	−	0.993018i	$-0.537635\pi$
$919$	−6572.58	−0.235919	−0.117959	+	0.993018i	$0.537635\pi$
$920$	−836.814	−0.0299880
$921$	−9598.82	−0.343422
$922$	−2064.05	−0.0737265
$923$	1709.64	0.0609681
$924$	−2292.89	−0.0816349
$925$	4536.52	0.161254
$926$	15676.5	0.556331
$927$	−7830.52	−0.277441
$928$	4685.84	0.165755
$929$	−29347.2	−1.03644	−0.518219	−	0.855248i	$-0.673405\pi$
$929$	−29347.2	−1.03644	−0.518219	+	0.855248i	$0.673405\pi$
$930$	6822.71	0.240565
$931$	−1846.30	−0.0649946
$932$	589.735	0.0207268
$933$	19627.3	0.688712
$934$	−23047.6	−0.807432
$935$	−14359.8	−0.502262
$936$	−1788.34	−0.0624507
$937$	−1420.98	−0.0495427	−0.0247714	−	0.999693i	$-0.507886\pi$
$937$	−1420.98	−0.0495427	−0.0247714	+	0.999693i	$0.507886\pi$
$938$	7157.68	0.249154
$939$	−9900.03	−0.344063
$940$	−1079.41	−0.0374536
$941$	38494.4	1.33356	0.666781	−	0.745254i	$-0.267672\pi$
$941$	38494.4	1.33356	0.666781	+	0.745254i	$0.267672\pi$
$942$	−11992.6	−0.414798
$943$	7113.10	0.245636
$944$	−315.480	−0.0108771
$945$	859.553	0.0295886
$946$	3471.42	0.119308
$947$	−50039.6	−1.71707	−0.858537	−	0.512752i	$-0.828626\pi$
$947$	−50039.6	−1.71707	−0.858537	+	0.512752i	$0.828626\pi$
$948$	2259.01	0.0773937
$949$	−22475.9	−0.768806
$950$	7861.21	0.268475
$951$	−19855.7	−0.677040
$952$	−6477.68	−0.220528
$953$	−20707.4	−0.703861	−0.351931	−	0.936026i	$-0.614475\pi$
$953$	−20707.4	−0.703861	−0.351931	+	0.936026i	$0.614475\pi$
$954$	−3018.54	−0.102441
$955$	−8846.83	−0.299766
$956$	7540.88	0.255115
$957$	11991.2	0.405038
$958$	−12461.5	−0.420265
$959$	6855.72	0.230847
$960$	−873.197	−0.0293566
$961$	32724.8	1.09848
$962$	2160.32	0.0724028
$963$	−6027.93	−0.201711
$964$	8089.93	0.270290
$965$	1331.88	0.0444299
$966$	−966.000	−0.0321745
$967$	−15818.6	−0.526053	−0.263027	−	0.964789i	$-0.584721\pi$
$967$	−15818.6	−0.526053	−0.263027	+	0.964789i	$0.584721\pi$
$968$	−4687.27	−0.155635
$969$	13075.5	0.433484
$970$	−15869.3	−0.525291
$971$	−11080.3	−0.366205	−0.183103	−	0.983094i	$-0.558614\pi$
$971$	−11080.3	−0.366205	−0.183103	+	0.983094i	$0.558614\pi$
$972$	−972.000	−0.0320750
$973$	−12086.3	−0.398222
$974$	17553.6	0.577469
$975$	−7773.08	−0.255321
$976$	−3126.02	−0.102522
$977$	2785.27	0.0912064	0.0456032	−	0.998960i	$-0.485479\pi$
$977$	2785.27	0.0912064	0.0456032	+	0.998960i	$0.485479\pi$
$978$	10293.2	0.336544
$979$	−28855.6	−0.942010
$980$	891.389	0.0290555
$981$	−7111.47	−0.231449
$982$	−21800.5	−0.708433
$983$	18173.8	0.589679	0.294840	−	0.955547i	$-0.404734\pi$
$983$	18173.8	0.589679	0.294840	+	0.955547i	$0.404734\pi$
$984$	7422.36	0.240464
$985$	3628.10	0.117361
$986$	33876.6	1.09417
$987$	−1246.05	−0.0401845
$988$	3743.56	0.120545
$989$	1462.51	0.0470225
$990$	−2234.54	−0.0717357
$991$	−58063.8	−1.86121	−0.930604	−	0.366029i	$-0.880717\pi$
$991$	−58063.8	−1.86121	−0.930604	+	0.366029i	$0.880717\pi$
$992$	−8001.01	−0.256081
$993$	−183.644	−0.00586884
$994$	963.640	0.0307493
$995$	−2278.73	−0.0726035
$996$	12275.0	0.390511
$997$	51829.6	1.64640	0.823200	−	0.567752i	$-0.192187\pi$
$997$	51829.6	1.64640	0.823200	+	0.567752i	$0.192187\pi$
$998$	−5919.00	−0.187738
$999$	1174.18	0.0371864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.e.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.e.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.54790 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.54790 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +9.09580 q^{10} -27.2964 q^{11} -12.0000 q^{12} -24.8381 q^{13} -14.0000 q^{14} -13.6437 q^{15} +16.0000 q^{16} +115.673 q^{17} +18.0000 q^{18} -37.6796 q^{19} +18.1916 q^{20} +21.0000 q^{21} -54.5927 q^{22} -23.0000 q^{23} -24.0000 q^{24} -104.317 q^{25} -49.6762 q^{26} -27.0000 q^{27} -28.0000 q^{28} +146.433 q^{29} -27.2874 q^{30} -250.032 q^{31} +32.0000 q^{32} +81.8891 q^{33} +231.346 q^{34} -31.8353 q^{35} +36.0000 q^{36} -43.4880 q^{37} -75.3591 q^{38} +74.5143 q^{39} +36.3832 q^{40} -309.265 q^{41} +42.0000 q^{42} -63.5876 q^{43} -109.185 q^{44} +40.9311 q^{45} -46.0000 q^{46} -59.3355 q^{47} -48.0000 q^{48} +49.0000 q^{49} -208.633 q^{50} -347.019 q^{51} -99.3525 q^{52} -167.696 q^{53} -54.0000 q^{54} -124.141 q^{55} -56.0000 q^{56} +113.039 q^{57} +292.865 q^{58} -19.7175 q^{59} -54.5748 q^{60} -195.376 q^{61} -500.063 q^{62} -63.0000 q^{63} +64.0000 q^{64} -112.961 q^{65} +163.778 q^{66} -511.263 q^{67} +462.692 q^{68} +69.0000 q^{69} -63.6706 q^{70} -68.8314 q^{71} +72.0000 q^{72} +904.894 q^{73} -86.9759 q^{74} +312.950 q^{75} -150.718 q^{76} +191.075 q^{77} +149.029 q^{78} -188.251 q^{79} +72.7664 q^{80} +81.0000 q^{81} -618.530 q^{82} -1022.92 q^{83} +84.0000 q^{84} +526.069 q^{85} -127.175 q^{86} -439.298 q^{87} -218.371 q^{88} +1057.12 q^{89} +81.8622 q^{90} +173.867 q^{91} -92.0000 q^{92} +750.095 q^{93} -118.671 q^{94} -171.363 q^{95} -96.0000 q^{96} -1744.68 q^{97} +98.0000 q^{98} -245.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 5 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 10 q^{10} - 56 q^{11} - 36 q^{12} + 29 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} + 28 q^{17} + 54 q^{18} - 18 q^{19} + 20 q^{20} + 63 q^{21} - 112 q^{22} - 69 q^{23} - 72 q^{24} + 32 q^{25} + 58 q^{26} - 81 q^{27} - 84 q^{28} - 242 q^{29} - 30 q^{30} - 86 q^{31} + 96 q^{32} + 168 q^{33} + 56 q^{34} - 35 q^{35} + 108 q^{36} - 70 q^{37} - 36 q^{38} - 87 q^{39} + 40 q^{40} - 402 q^{41} + 126 q^{42} - 553 q^{43} - 224 q^{44} + 45 q^{45} - 138 q^{46} - 368 q^{47} - 144 q^{48} + 147 q^{49} + 64 q^{50} - 84 q^{51} + 116 q^{52} + 23 q^{53} - 162 q^{54} - 467 q^{55} - 168 q^{56} + 54 q^{57} - 484 q^{58} - 861 q^{59} - 60 q^{60} - 311 q^{61} - 172 q^{62} - 189 q^{63} + 192 q^{64} - 624 q^{65} + 336 q^{66} - 215 q^{67} + 112 q^{68} + 207 q^{69} - 70 q^{70} + 121 q^{71} + 216 q^{72} - 588 q^{73} - 140 q^{74} - 96 q^{75} - 72 q^{76} + 392 q^{77} - 174 q^{78} - 1418 q^{79} + 80 q^{80} + 243 q^{81} - 804 q^{82} - 352 q^{83} + 252 q^{84} - 827 q^{85} - 1106 q^{86} + 726 q^{87} - 448 q^{88} + 1275 q^{89} + 90 q^{90} - 203 q^{91} - 276 q^{92} + 258 q^{93} - 736 q^{94} - 3593 q^{95} - 288 q^{96} - 602 q^{97} + 294 q^{98} - 504 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 5 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 10 * q^10 - 56 * q^11 - 36 * q^12 + 29 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 + 28 * q^17 + 54 * q^18 - 18 * q^19 + 20 * q^20 + 63 * q^21 - 112 * q^22 - 69 * q^23 - 72 * q^24 + 32 * q^25 + 58 * q^26 - 81 * q^27 - 84 * q^28 - 242 * q^29 - 30 * q^30 - 86 * q^31 + 96 * q^32 + 168 * q^33 + 56 * q^34 - 35 * q^35 + 108 * q^36 - 70 * q^37 - 36 * q^38 - 87 * q^39 + 40 * q^40 - 402 * q^41 + 126 * q^42 - 553 * q^43 - 224 * q^44 + 45 * q^45 - 138 * q^46 - 368 * q^47 - 144 * q^48 + 147 * q^49 + 64 * q^50 - 84 * q^51 + 116 * q^52 + 23 * q^53 - 162 * q^54 - 467 * q^55 - 168 * q^56 + 54 * q^57 - 484 * q^58 - 861 * q^59 - 60 * q^60 - 311 * q^61 - 172 * q^62 - 189 * q^63 + 192 * q^64 - 624 * q^65 + 336 * q^66 - 215 * q^67 + 112 * q^68 + 207 * q^69 - 70 * q^70 + 121 * q^71 + 216 * q^72 - 588 * q^73 - 140 * q^74 - 96 * q^75 - 72 * q^76 + 392 * q^77 - 174 * q^78 - 1418 * q^79 + 80 * q^80 + 243 * q^81 - 804 * q^82 - 352 * q^83 + 252 * q^84 - 827 * q^85 - 1106 * q^86 + 726 * q^87 - 448 * q^88 + 1275 * q^89 + 90 * q^90 - 203 * q^91 - 276 * q^92 + 258 * q^93 - 736 * q^94 - 3593 * q^95 - 288 * q^96 - 602 * q^97 + 294 * q^98 - 504 * q^99

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